APPLICATION OF A NOVEL VARIABLE-ORDER FRACTIONAL NEUTRON POINT KINETICS MODEL FOR NUCLEAR REACTOR REACTIVITY TRANSIENT ANALYSIS

This work introduces a novel Variable-order Fractional Neutron Point Kinetics (VFONPK) model, grounded in Scarpi’s fractional calculus approach, for the analysis of nuclear reactor dynamics. The proposed framework specifically examines neutron density behavior during reactivity transients, with a focused investigation of both delayed neutron precursor density and total neutron density dynamics. Two key simulation scenarios are examined: reactivity insertion and reactor startup dynamics, based on solutions of both constant-order and variable-order fractional kinetics equations. Notably, our findings indicate pronounced differences in neutron density oscillations, particularly in relation to varying anomalous diffusion order (related to the order of the derivative operators). Low-frequency alterations in the diffusion order induce significant oscillatory behavior in neutron density, whereas high-frequency variations tend to suppress these oscillations. Moreover, our results reveal that low-frequency oscillations in the diffusion order (time variable order) lead to a “long-term” memory effect on neutron density, while high-frequency oscillations produce immediate fluctuations, indicative of “short-term” memory effects. These insights underscore the critical necessity of incorporating variable-order fractional derivatives in models of nuclear kinetics to enhance our comprehension of reactor core neutronic dynamics under transient conditions.